Zonal jets and inertia–gravity waves are ubiquitous on planets such as Earth, Jupiter and Saturn. Motivated by the modification of energy flux of balanced flow by inertia–gravity waves, this paper studies the impact of near-inertial waves (NIWs) on zonal jets on a $\beta$-plane. Using a two-dimensional quasi-geostrophic and NIW coupled system on a $\beta$-plane (Xie & Vanneste, J. Fluid Mech., vol. 774, 2015, pp. 143–169), we find NIWs catalytically impact several features of zonal jets. The NIWs inhibit jet formation due to the waves’ catalytic induction of downscale mean energy flux. As the strength of NIWs increases, a critical point exists beyond which zonal jets are annihilated. The jet spacing is captured by the Rhines scale $L\sim \sqrt {U/\beta }$ with $U$ estimated from the upscale energy flux induced by the mean flow alone, which again shows that the NIWs’ impact is catalytic. Also, the temporal asymmetry of NIWs leads to the spatial asymmetry of jet dynamics. The jet profiles are asymmetric with a stronger shear on the left flank. And similar to the left turning of vortex dipole under the impact of NIWs, the NIW-modified jets migrate poleward. The NIWs also show a catalytic role in jet migration: the net momentum flux directly induced by NIWs is of secondary importance in the zonal mean momentum dynamics and impedes jet migration, while the advective effect of NIW-modified mean flow dominates the jet migration velocity.

The existence of Bolgiano–Obukhov (BO) scaling in Rayleigh–Bénard convection (RBC) has long been speculated. However, due to the inhomogeneity and anisotropy of the flow, and the lack of clear scale separation, no conclusive evidence has been found. To avoid these non-ideal factors, we construct an idealized isotropic convection system by introducing an additional horizontal buoyancy field to RBC in a doubly periodic domain. We focus on the two-dimensional case so that its upscale kinetic energy flux can enable a long inertial range for detecting the BO scaling. Through direct numerical simulations of this system, we justify the existence of BO scaling using second- and third-order structure functions, which are in good agreement with our theoretically obtained scaling relations from the Kármán–Howarth–Monin equations. These theoretical and numerical results provide direct support for the conjecture that the existence of the BO scaling in RBC is associated with the inverse kinetic energy cascade. For higher-order structure functions, we found strong intermittent effects in the buoyancy field, but not in the velocity. By comparing the present system with the canonical anisotropic RBC in a periodic domain, the effects of anisotropy on the scaling properties are elucidated.

Wind forcing injects energy into mesoscale eddies and near-inertial waves (NIWs) in the ocean, and the NIWs are believed to solve the puzzle of mesoscale energy budget by absorbing energy from mesoscale eddies. This work studies the turbulent energy transfer in the NIW–quasigeostrophic mean mesoscale eddy coupled system based on a previously derived two-dimensional model which inherits conserved quantities in Boussinesq equations (Xie & Vanneste, J. Fluid Mech., vol. 774, 2015, pp. 147–169). The conservation of energy, potential enstrophy and wave action implies the existence of phase transition with a change of the relative strength between NIW and mean-flow, quantified by a parameter $R$. By running forced-dissipative numerical simulations, we justify the existence of second-order phase transition around a critical value $R_c$. When $0<R<R_c$, energy transfers bidirectionally, wave action transfers downscale and vorticity forms strong cyclones. When $R>R_c$, energy transfers downscale, wave action transfers bidirectionally and vortex filaments are dominant. We find the catalytic wave induction mechanism where the NIW induces a downscale energy flux of the mean flow, which differs from the stimulated loss of balance mechanism observed in inertial value problems. In the parameter regime $0<R<R_c$, catalytic wave induction is similar to the stimulated loss of balance as the downscale energy transfer is proportional to the NIW energy injection, however, catalytic wave induction has a distinct feature of the absence of energy conversion from mesoscale eddies to NIWs. The new mechanism is effective in the toy-model study, making it potentially important for ocean energetics.

Previous nutritional studies have shown that insulin regulation is different between DT and A strains of gibel carp. As leptin plays a pivotal role in the effects of insulin, we hypothesised that leptin regulation of glucose and lipid metabolism would differ between the two strains. To test our hypothesis, recombinant human leptin was injected into two strains. The results showed that leptin activated the phosphatidylinositol 3-kinase (PI3K)–protein kinase B (AKT), AMP-activated protein kinase–acetyl coenzyme A carboxylase and Janus kinase 2 (JAK2)–signal transducer and activator of transcription (STAT) signalling pathways in both strains. Hypoglycaemia induced by leptin might be due to higher glucose uptake by the liver and muscles together with enhanced glycolytic potential and reduced gluconeogenic potential. Decreased lipogenesis and up-regulated fatty acid oxidation were induced by leptin. In terms of genotype, the PI3K–AKT signalling pathway was more strongly activated by leptin in the muscle tissue of the A strain, as reflected by the heightened phosphorylation of AKT. Furthermore, glycogen content, glycolytic enzyme activity and gluconeogenic capability were higher in the A strain than the DT strain. Strain A had higher levels of fatty acid synthesis and lipolytic capacity in the liver than the DT strain, but the opposite was true in white muscle. Regarding leptin–genotype interactions, the DT strain displayed stronger regulation of glucose metabolism in the liver by leptin as compared with the A strain. Moreover, a more active JAK2–STAT signalling pathway accompanied by enhanced inhibition of fatty acid synthesis by leptin was observed in the DT strain. Overall, the regulation of glucose and lipid metabolism by leptin differed between the two strains, as expected.

The clinical characteristics of patients with COVID-19 were analysed to determine the factors influencing the prognosis and virus shedding time to facilitate early detection of disease progression. Logistic regression analysis was used to explore the relationships among prognosis, clinical characteristics and laboratory indexes. The predictive value of this model was assessed with receiver operating characteristic curve analysis, calibration and internal validation. The viral shedding duration was calculated using the Kaplan–Meier method, and the prognostic factors were analysed by univariate log-rank analysis and the Cox proportional hazards model. A retrospective study was carried out with patients with COVID-19 in Tianjin, China. A total of 185 patients were included, 27 (14.59%) of whom were severely ill at the time of discharge and three (1.6%) of whom died. Our findings demonstrate that patients with an advanced age, diabetes, a low PaO2/FiO2 value and delayed treatment should be carefully monitored for disease progression to reduce the incidence of severe disease. Hypoproteinaemia and the fever duration warrant special attention. Timely interventions in symptomatic patients and a time from symptom onset to treatment <4 days can shorten the duration of viral shedding.

An oral starch administration trial was used to evaluate glucose homoeostasis in grass carp (Ctenopharyngodon idella) and Chinese longsnout catfish (Leiocassis longirostris Günther). Fish were administered with 3 g of a water and starch mixture (with 3:2 ratio) per 100 g body weight after fasting for 48 h. Fish were sampled at 0, 1, 3, 6, 12, 24 and 48 h after oral starch administration. In grass carp, plasma levels of glucose peaked at 3 h but returned to baseline at 6 h. However, in Chinese longsnout catfish, plasma glucose levels peaked at 6 h and returned to baseline at 48 h. The activity of intestinal amylase was increased in grass carp at 1 and 3 h, but no significant change in Chinese longsnout catfish was observed. The activity of hepatic glucose-6-phosphatase fell significantly in grass carp but change was not evident in Chinese longsnout catfish. The expression levels and enzymic activity of hepatic pyruvate kinase increased in grass carp, but no significant changes were observed in the Chinese longsnout catfish. Glycogen synthase (gys) and glycogen phosphorylase (gp) were induced in grass carp. However, there was no significant change in gys and a clear down-regulation of gp in Chinese longsnout catfish. In brief, compared with Chinese longsnout catfish, grass carp exhibited a rapid increase and faster clearance rate of plasma glucose. This effect was closely related to significantly enhanced levels of digestion, glycolysis, glycogen metabolism and glucose-induced lipogenesis in grass carp, as well as the inhibition of gluconeogenesis.

We derive and test a new heuristic theory for third-order structure functions that resolves the forcing scale in the scenario of simultaneous spectral energy transfer to both small and large scales, which can occur naturally, for example, in rotating stratified turbulence or magnetohydrodynamical (MHD) turbulence. The theory has three parameters – namely the upscale/downscale energy transfer rates and the forcing scale – and it includes the classic inertial-range theories as local limits. When applied to measured data, our global-in-scale theory can deduce the energy transfer rates using the full range of data, therefore it has broader applications compared with the local theories, especially in situations where the data is imperfect. In addition, because of the resolution of forcing scales, the new theory can detect the scales of energy input, which was impossible before. We test our new theory with a two-dimensional simulation of MHD turbulence.

We present an idealized study of rotating stratified wave turbulence in a two-dimensional vertical slice model of the Boussinesq equations, focusing on the peculiar case of equal Coriolis and buoyancy frequencies. In this case the fully nonlinear fluid dynamics can be shown to be isotropic in the vertical plane, which allows the classical methods of isotropic turbulence to be applied. Contrary to ordinary two-dimensional turbulence, here a robust downscale flux of total energy is observed in numerical simulations that span the full parameter regime between Ozmidov and forcing scales. Notably, this robust downscale flux of the total energy does not hold separately for its various kinetic and potential components, which can exhibit both upscale and downscale fluxes, depending on the parameter regime. Using a suitable extension of the classical Kármán–Howarth–Monin equation, exact expressions that link third-order structure functions and the spectral energy flux are derived and tested against numerical results. These expressions make obvious that even though the total energy is robustly transferred downscale, the third-order structure functions are sign indefinite, which illustrates that the sign and the form of measured third-order structure functions are both crucially important in determining the direction of the spectral energy transfer.

Large-scale coherent structures such as jets in Rayleigh–Bénard convection and related systems are receiving increasing attention. This paper studies, both numerically and theoretically, the process of jet formation in two-dimensional salt-finger convection. The approach utilizes an asymptotically derived system of equations referred to as the modified Rayleigh–Bénard convection (MRBC) model, valid in the geophysically and astrophysically relevant limit in which the solute diffuses much more slowly than heat. In these equations, convection is driven by a destabilizing salinity gradient while the effects of the stabilizing temperature gradient manifest themselves as an additional anisotropic dissipation acting on large scales. The MRBC system is specified by two external parameters: the Schmidt number $\mathit{Sc}$ (ratio of viscosity to solutal diffusivity) and the Rayleigh ratio $\mathit{Ra}$ (ratio between the Rayleigh numbers of the destabilizing solutal stratification and the stabilizing thermal stratification). Two distinct $\mathit{Ra}$ regimes are explored for fixed $\mathit{Sc}=1$. In all cases studied the system develops a horizontal jet structure that is maintained self-consistently by turbulent fluctuations, but coarsens over time. For intermediate Rayleigh ratios (e.g. $\mathit{Ra}=6$), the MRBC model captures the relaxation oscillations superposed on the jet structure observed at similar parameter values in direct numerical simulations of the primitive equations. For smaller Rayleigh ratios (e.g. $\mathit{Ra}=2$), a regime for which direct numerical simulation of the primitive equations is difficult because of the presence of fast gravity waves, the MRBC model reveals the existence of statistically steady jets whose properties are studied in detail. Three hierarchical models, the MRBC and further reductions in the form of quasilinear and single-mode approximations, are used to confirm that jets form and are sustained as a result of the interaction between fluctuations (salt fingers) and large-scale horizontally averaged horizontal flows (jets). Even though the small-scale structures exhibited by the three models exhibit clear differences, all three produce the same power-law spectrum of the mean fields at large vertical scales: in all, the spectrum of the mean streamfunction scales as $m^{-3}$ and the mean salinity field scales as $m^{-1}$, with $m$ the vertical wavenumber. A theoretical explanation of these observations based on the dominant balances in the mean and fluctuation equations is provided. As a consequence, the jets have a zigzag profile, a conclusion that is consistent with numerical simulations. Based on numerical observations, a three-component phenomenological model consisting of a linearly growing mode, a linearly damped mode and a mean mode is proposed to explain the observed transition from statistically steady jet structure to jets with superposed oscillations that takes place with increasing Rayleigh ratio.

Several epidemiological studies have investigated that Na or K intakes might be associated with the metabolic syndrome (MetS). However, little evidence has evaluated the association between Na:K ratio and the MetS. In this study, we assessed the association between the dietary Na:K ratio and the MetS. The cross-sectional study was conducted among adults aged 18 years and older in Nanjing, using a multi-stage random sampling method, which resulted in a sample size of 1993 participants. Dietary Na and K intakes were assessed by 3 consecutive days of dietary recollection combined with condiments weighing method. Health-related data were obtained by standardised questionnaires, as well as physical examinations and laboratory assessments. The prevalence rate of the MetS was 36·5 % (728/1993). After adjusting for various lifestyle and dietary factors of the MetS, participants in the highest quartile of dietary Na:K ratio were at a higher risk of developing MetS (OR=1·602; 95 % CI 1·090, 2·353) compared with those in the lowest quartile. Each 1-sd increase in dietary Na:K ratio was associated with a higher risk of prevalent MetS (OR=1·166; 95 % CI: 1·018, 1·336). Among the components of the MetS, dietary Na:K ratio was positively associated with high blood pressure (quartile 3 v. quartile 1: OR=1·656; 95 % CI 1·228, 2·256) and hypertriacylglycerolaemia (quartile 4 v. quartile1: OR=1·305; 95 % CI 1·029, 1·655) in multivariate analysis. These results revealed that higher dietary Na:K ratio significantly increased the risk of the MetS in Chinese adults. Further studies are needed to verify this association.

We derive and investigate exact expressions for third-order structure functions in stationary isotropic two-dimensional turbulence, assuming a statistical balance between random forcing and dissipation both at small and large scales. Our results extend previously derived asymptotic expressions in the enstrophy and energy inertial ranges by providing uniformly valid expressions that apply across the entire non-dissipative range, which, importantly, includes the forcing scales. In the special case of white noise in time forcing this leads to explicit predictions for the third-order structure functions, which are successfully tested against previously published high-resolution numerical simulations. We also consider spectral energy transfer rates and suggest and test a simple robust diagnostic formula that is useful when forcing is applied at more than one scale.

Mountain-generated inertia–gravity waves (IGWs) affect the dynamics of both the atmosphere and the ocean through the mean force they exert as they interact with the flow. A key to this interaction is the presence of critical-level singularities or, when planetary rotation is taken into account, inertial-level singularities, where the Doppler-shifted wave frequency matches the local Coriolis frequency. We examine the role of the latter singularities by studying the steady wavepacket generated by a multiscale mountain in a rotating linear shear flow at low Rossby number. Using a combination of Wentzel–Kramers–Brillouin (WKB) and saddle-point approximations, we provide an explicit description of the form of the wavepacket, of the mean forcing it induces and of the mean-flow response. We identify two distinguished regimes of wave propagation: Regime I applies far enough from a dominant inertial level for the standard ray-tracing approximation to be valid; Regime II applies to a thin region where the wavepacket structure is controlled by the inertial-level singularities. The wave–mean-flow interaction is governed by the change in Eliassen–Palm (or pseudomomentum) flux. This change is localised in a thin inertial layer where the wavepacket takes a limiting form of that found in Regime II. We solve a quasi-geostrophic potential-vorticity equation forced by the divergence of the Eliassen–Palm flux to compute the wave-induced mean flow. Our results, obtained in an inviscid limit, show that the wavepacket reaches a large-but-finite distance downstream of the mountain (specifically, a distance of order $(k_{\ast }\unicode[STIX]{x1D6E5})^{1/2}\unicode[STIX]{x1D6E5}$, where $k_{\ast }^{-1}$ and $\unicode[STIX]{x1D6E5}$ measure the wave and envelope scales of the mountain) and extends horizontally over a similar scale.

Nanoindentation was performed on amorphous silicon nitride films of different thicknesses deposited on gallium arsenide (GaAs) (001) substrates using a conical indenter. Both “pop-in” and ‘pop-out’ were observed from the load-displacement curves when the indentation load exceeded a critical value. Pop-in occurring during loading is associated with plane-slip in the GaAs substrate, and pop-out during unloading is attributed to the interfacial delamination between the film and the substrate. Finite element modeling (FEM) was used to analyze the stress evolution during unloading. The FEM results showed that the stress at the interface evolved from compressive to tensile status during the withdrawal of indentation load, and the interfacial debonding was induced at a critical tensile stress, which is consistent with the pop-out observed. A deformation model for interpreting the pop-in and pop-out events is thereby proposed.